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Find the zeros of the function. Enter the solutions from least to greatest.

{:[h(x)=(-2x+3)(-x+3)],[" lesser "x=◻],[" greater "x=◻]:}

Find the zeros of the function. Enter the solutions from least to greatest. $\newline$ $h(x) = (-2x + 3)(-x + 3)$ , $\text{lesser } x = \square$ , $\text{greater } x = \square$

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Find the roots of factored polynomials

Full solution

Q. Find the zeros of the function. Enter the solutions from least to greatest.

\newline

h(x) = (-2x + 3)(-x + 3)

,

\text{lesser } x = \square

,

\text{greater } x = \square

Factored function: Factored function: $h(x) = (-2x + 3)(-x + 3)$ $\newline$ To find the zeros of the function, we need to set the function equal to zero and solve for $x$ . $\newline$ $(-2x + 3)(-x + 3) = 0$
First zero: First zero: Solve $-2x + 3 = 0$
Subtract $3$ from both sides:
$-2x + 3 - 3 = 0 - 3$
$-2x = -3$
Now divide both sides by $-2$ :
$x = \frac{-3}{-2}$
$x = \frac{3}{2}$
Second zero: Second zero: Solve $-x + 3 = 0$
Subtract $3$ from both sides:
$-x + 3 - 3 = 0 - 3$
$-x = -3$
Now multiply both sides by $-1$ :
$x = -3 \times -1$
$x = 3$
List of zeros: We have found the two zeros of the function: $\newline$ $x = \frac{3}{2}$ $\newline$ $x = 3$ $\newline$ Now we need to list them from least to greatest. $\newline$ $\frac{3}{2}$ is less than $3$ , so the correct order is: $\newline$ $\frac{3}{2}, 3$

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